A rondom Variable x takes value X; with Probabil Pi with i=1 labelling all possibilities. The m N
A rondom Variable x takes value X; with Probabil Pi with i=1 labelling all possibilities. The m N
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Tate: /20
A rondom Variable x takes value X; with Probability
Pi, with i = 1,... N labelling all possibilities. The mean
Value of x is given,
N
X = ² ½ Pixi
1
Ni=
And Shonon entropy of x
S(x)=
11
-
is
N
S
i=1
Pi
P₁ =
given as,
Pilog Pi
L
Find distribution which maximises the shonon entropy
for a fixed value of meon X. Formulate this as
a Longsonge multiplier problem and show that
the distribution which solves it has form,
1PXi
447
Z
where, B and 7 Con² in principle (but may be
not
in practise) be found in teams of values
{X j }, X and N-
9
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